A



William Paterson University of New Jersey

College of Science and Health

Department of Mathematics

- Course Outline –

1. Title of Course, Course Number and Credits:

MATH3260 Mathematical Models in Finance I - 3 credits

2. Description of Course:

A course on the formulation, analysis, and interpretation of advanced mathematical models in finance and interest theory. Technology will be used to give students a hands-on experience in developing and solving their own models. The course will cover the basic fundamentals needed for the second actuarial exam. Applications to "real-world" problems in interest theory, including the development of complex annuity models, will also be studied. Although primary focus will be on the application of financial models developed in Kellison, the mathematical derivation and analysis of the formulae will also be covered.

Financial models studied will include: the accumulation function and the special cases of simple and compound interest; nominal and effective interest and discount rates, and the force of interest –both constant and varying; Valuation of discrete and continuous streams of payments, including the case in which the interest conversion period differs from the payment period; geometrically and arithmetically varying annuity models; application of interest theory to amortization of lump sums, depreciation, mortgages, and additional financial models.

3. Course Prerequisites:

Math 2010 - Calculus III (C+ or better) or Math 2020 Linear Algebra (C+ or better)

4. Course Objectives:

The student will obtain a practical knowledge of the basic theory of interest in both discrete and continuous time.

1. The student will understand how the concepts or interest theory are used in the various annuity functions.

2. The student will apply the concepts of present and accumulated value for the various streams of payments.

3. Students will be able to define and recognize the definitions of the following terms: interest rate, simple interest, compound interest, accumulation function, future value, current value, present value, net present value, discount factor, discount rate, convertible (compounded) m-thly, nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value, annuity-immediate, annuity due, perpetuity, payable m-thly or payable continuously, level payment annuity, arithmetic increasing/decreasing annuity, geometric increasing/decreasing annuity, term of annuity, principal, interest, term of loan, outstanding balance, final payment (drop payment or balloon payment), amortization, sinking fund.

4. Given any one of the following rates of interest, effective rate, nominal rate convertible m-thly, effective discount rate, the nominal discount rate convertible m-thly, or the force of interest, students will be able to calculate any of the other rates. Students will learn to develop and solve equations of value and time value of money equations involving simple interest, compound interest or variable force of interest. Students will learn to solve level and non-level annuity problems including arithmetic and geometric progression annuities. Students will also learn to solve loan problems including finding the required payment period, principal, interest rate, or the outstanding balance at any point in time.

| |

5. Student Learning Outcomes:

Students will be able to:

1. Calculate equivalent rates of interest. This will be assessed through quizzes, tests and a final exam.

2. Understand the basic concepts of present value and accumulated value and apply these concepts toward solving more complicated financial problems and complex annuity problems. This will be assessed through quizzes, tests and a final exam.

3. Work effectively with others to complete homework and class projects. This will be assessed through class projects.

4. Locate and use information to solve problems in interest theory and financial engineering. This will be assessed through quizzes and tests, and a final exam.

5. Effectively express themselves both orally and in writing using well constructed mathematical arguments. This will be assessed through class projects, quizzes, and tests and a final exam.

6. Demonstrate ability to think critically by recognizing patterns and determining and appropriate techniques for solving a variety of annuity and interest theory problems. This will be assessed through quizzes, tests and a final exam.

7. Demonstrate the ability to integrate knowledge and ideas of the concepts of present and accumulated value in a coherent and meaningful manner and apply a variety of techniques for solving such problems. This will be assessed through homework, class quizzes and tests, and a final exam.

6. Topical Outline of the Course Content:

Chapter 1 - The Measurement of Interest

1.1 Introduction

1.2 The Accumulation and Amount Functions

1.3 The Effective Rate of Interest

1.4 Simple Interest

1.5 Compound Interest

1.6 Present Value

1.7 The Effective Rate of Discount

1.8 Nominal Rates of Interest and Discount

1.9 Forces of Varying Interest and Discount

1.10 Varying Interest

1.11 Summary of Results

Chapter 2 - Solutions of Problems in Interest

2.1 Introduction

2.2 The Basic Problem

2.3 Equations of Value

2.4 Unknown Time

2.5 Unknown Rate of Interest

2.6 Determining Time Periods

Chapter 3 - Basic Annuities

3.1 Introduction

3.2 Annuity-Immediate

3.3 Annuity-Due

3.4 Annuity Values on Any Date

3.5 Perpetuities

3.6 Unknown Time

3.7 Unknown Rate of Interest

3.8 Varying Interest

Chapter 4 - More General Annuities

4.1 Introduction

4.2 Differing payment and Interest Conversion Periods

4.3 Annuities Payable Less Frequently than Interest is Convertible

4.4 Annuities Payable More Frequently than Interest is Convertible

4.5 Continuous Annuities

4.6 Payments Varying in Arithmetic Progression

4.7 Payments Varying in Geometric Progression

4.8 More General Varying Annuities

4.9 Continuous Varying Annuities

4.10 Summary of Results

Chapter 5 Amortization Schedules and Sinking Funds

5.1 Introduction

5.2 Finding the Outstanding Loan Balance

5.3 Amortization Schedules

5.4 Sinking Funds

5.5 Differing Payment Periods and Interest Conversion Periods

5.6 Varying Series of Payments

Chapter 6 - Bonds and Other Securities *

1. Introduction

2. Types of Securities

3. Price of a Bond

4. Premium and Discount

5. Valuation Between Coupon Payment Dates

6. Determination of Yield Rates

7. Callable and Putable Bonds

* Selected topics on will be covered at the discretion of the instructor.

7. Guidelines/Suggestions for Teaching Methods and Student Learning Activities:

The course will be a combination of formal lectures, calculator and/or computer laboratory exercises, and group projects. Both calculators and computers will be used to illustrate and enhance concepts and to solve some of the more intricate financial models.

8. Guidelines/Suggestions for Methods of Student Assessment

(Student Learning Outcomes)

There will be regularly announced quizzes, 2 tests and a final examination.

9. Suggested Reading, Texts and Objects of Study:

Kellison, S., The Theory of Interest, Third Edition, Irwin Press, 2009

Calculator: The BA-35 (Business Analyst) by Texas Instrument.

10. Bibliography of Supportive Texts and Other Materials:

Broverman, S.A., Mathematics of Investment and Credit (Fifth Edition), 2010, ACTEX Publications

Ruckman, C.; and Francis, J., Financial Mathematics: A Practical Guide for Actuaries and other

Business Professionals (Second Edition), 2005, BPP Professional Education

10. Preparer’s Name and Date:

Donna J. Cedio-Fengya - Spring 2015

11. Original Department Approval Date:

Fall 2015

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download